Graph the function defined by the parametric equations

Answer
Start out with a table of values, to have an idea of what's going on:

Plot and connect the points we have:

From t = 0 to t = π we have a quarter circle. That means it will take until t = 4π to find the complete circle:

As t goes from 4π to 8π, the etch-a-sketch tip will go around the circle again: